Problem: Simplify the following expression: $ r = \dfrac{6t + 5}{t - 9} + 4 $
Solution: In order to subtract expressions, they must have a common denominator. Multiply the second expression by $\dfrac{t - 9}{t - 9}$ $ \dfrac{-4}{1} \times \dfrac{t - 9}{t - 9} = \dfrac{-4t + 36}{t - 9} $ Therefore $ r = \dfrac{6t + 5}{t - 9} - \dfrac{-4t + 36}{t - 9} $ Now the expressions have the same denominator we can simply subtract the numerators: $r = \dfrac{6t + 5 - (-4t + 36) }{t - 9} $ Distribute the negative sign: $r = \dfrac{6t + 5 + 4t - 36}{t - 9}$ $r = \dfrac{10t - 31}{t - 9}$